Can I use a name that is trademarked in a different class?

Sometimes, but the class number alone does not decide it. Examiners ask whether the goods are related: whether buyers would think they come from the same source. Goods in different classes can still be related, such as coffee and cafes, or clothing and bags. LogoVerify weighs your own class first, then the classes the USPTO itself lists as coordinated (related), and says when the answer depends on what you sell. A trademark attorney can tell you whether a specific overlap matters. (General information, not legal advice.)